There a great write-up on these interesting tokens at DumpDiggers blog which says, in summary,

Philip Bowes Vere Broke became a Captain in the Royal Navy in 1801, but he didnít get his own ship until 1806 - that was the year Broke took command of the HMS Shannon, a 38 gun frigate.

Six years later, Captain Broke was stationed in Halifax when war erupted between England and the American States. Broke sailed south and blockaded Boston, wherein he could see the larger USS Chesapeake.

The two ships engaged in single combat. Captain Broke captured his enemy after less than twenty minutes of naval combat. The Chesapeake suffered early in the exchange of broadsides, having its wheel shot away. Without any maneuverability the more powerful American warship was helpless to resist Captain Broke's final assault.

You can find these tokens for sale on eBay. Typical catalog values run like this: